(CNN) - Sony Entertainment CEO Michael Lynton, denying that the studio had "caved" by scrapping next week's opening of "The Interview," fired back Friday after President Obama said the studio had "made a mistake."

In an exclusive interview with CNN's Fareed Zakaria, Lynton also reopened the door to a future release of the controversial comedy, saying the company is considering some sort of release on the Internet.

Sony followed up on Lynton's remarks with a statement that read, in part, "It is still our hope that anyone who wants to see this movie will get the opportunity to do so."

The company declined to comment on whether any distributors have agreed to help the company with that.

In his CNN interview, Lynton said "the president, the press and the public are mistaken" about what actually led to Sony's decision to shelve the "The Interview."

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